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Investigation of multicollinearity allows parameters in multivariate analysis to be estimated with higher precision and with biological interpretation. In order to generate reliable estimates of the degree of multicollinearity, it is necessary to use appropriate sample size. Thus, the objectives of this study were to determine the sample size (number of plants) necessary to estimate the indicators of the degree of multicollinearity - condition number (CN), correlation matrix determinant (DET), and variance inflation factor (VIF) - in morphological traits of rye and to verify the variability of the sample size between the indicators. Five and three uniformity trials were conducted with the cultivars BRS Progresso and Temprano, respectively. Eight morphological traits were evaluated in 780 plants in eight trials. For each trial, 22 cases were selected among the 28 formed by the combination of eight traits, taken six by six, totaling 176 cases. In each case, 197 sample sizes were planned (20, 25, 30, ..., 1,000 plants) and in each size 2,000 resampling procedures with replacement were performed, CN, DET, and VIF were determined and the average among 2,000 estimates was calculated. For each case and indicator (CN, DET, and VIF), the sample size was determined through three models: modified maximum curvature method and linear and quadratic segmented models with plateau response. There is variability between sample sizes between indicators, with larger sample sizes required for DET, followed by CN and VIF, in that order, with at least 180, 116 and 85 plants, respectively. A investigação da multicolinearidade permite que parâmetros em análises multivariadas sejam estimados com maior precisão e com interpretação biológica. Para ter confiabilidade nas estimativas do grau de multicolinearidade, é necessário utilizar adequado tamanho de amostra. Assim, os objetivos deste trabalho foram determinar o tamanho de amostra (número de plantas) necessário para a estimação dos indicadores do grau de multicolinearidade - número de condição (NC), determinante da matriz de correlação (DET) e fator de inflação da variância (FIV) - em caracteres morfológicos de centeio e verificar a variabilidade do tamanho de amostra entre os indicadores. Foram conduzidos cinco e três ensaios de uniformidade com as cultivares BRS Progresso e Temprano, respectivamente. Foram avaliados oito caracteres morfológicos em 780 plantas em oito ensaios. Para cada ensaio, foram selecionados 22 casos entre os 28 formados pela combinação de oito caracteres, tomados seis a seis, totalizando 176 casos. Para cada caso, foram planejados 197 tamanhos de amostra (20, 25, 30, ..., 1.000 plantas) e para cada tamanho foram realizadas 2.000 reamostragens, com reposição, determinados o NC, DET e FIV e calculada a média das 2.000 estimativas. Após, para cada caso e indicador, foi determinado o tamanho de amostra, por meio de três modelos: método da máxima curvatura modificado e modelos linear e quadrático segmentados com resposta em platô. Há variabilidade entre os tamanhos de amostra entre os indicadores, com necessidade de maiores tamanhos de amostra para DET, seguido de NC e FIV, nessa ordem, com no mínimo de 180, 116 e 85 plantas, respectivamente.

The objective of this study was to determine the optimal plot size to evaluate the mass of fresh matter in millet (Pennisetum glaucum L.) and showy rattlebox (Crotalaria spectabilis Roth.), in scenarios formed by combinations of treatment numbers, repetitions numbers, and levels of experimental precision. Fifteen uniformity trials with millet and showy rattlebox, in single or intercropping, were carried out. The mass of fresh matter was evaluated in 540 basic experimental units (BEU) of 1 × 1 m (15 trials × 36 BEU per trial). The heterogeneity index of Smith (1938) was estimated. The plot size was determined by the method of Hatheway (1961) in scenarios formed by combinations of i treatments (i = 5, 10, 15, 20, and 25), r repetitions (r = 3, 4, 5, 6, 7, 8, 9, and 10), and d precision levels (d = 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, and 20%). To evaluate the mass of fresh matter of millet and showy rattlebox, in single or intercropping, with 5 to 25 treatments and with five repetitions, plots of 10 m² of useful area are sufficient for differences between treatments of 9% of the overall average of the experiment to be considered significant at 0.05 probability.

This study aimed to verify the linear relationships between maize grain yield and tassel traits, identify traits for selection through direct and indirect effects over three crop years. Three experiments were performed with 20 maize genotypes in a randomized complete block design with three replicates. Individual variance analysis showed significant genotype effects for all traits in the three crop years. However, a joint analysis demonstrated a significant genotype effect at 5% error probability for all traits, but branching space length. Furthermore, only the number of secondary branches and tassel branch number did not show significant genotype × crop year interaction. These results revealed a genotype differentiated behavior over the evaluated years, emphasizing the need to evaluate genotypes in more than one crop year. Based on phenotypic and genotypic correlation matrices and path analyses, the number of secondary tassel branches showed a positive linear relationship with grain yield; therefore, it can be used for the indirect selection of maize plants in breeding programs

The objectives of this study were to evaluate the agronomic performance of nine lettuce cultivars (Gloriosa, Pira Verde, Stella, Ceres, Grandes Lagos, Rubinella, Crocantela, Elisa and Vera), in three seasons (autumn-winter, spring and summer) and evaluate the effect of shade netting in spring and summer. Ten experiments were carried out, using the soilless cultivation systems in a sheltered environment. The experimental design was completely randomized, six benches were used in the autumn-winter season and four in both spring and summer, with 44 pots per bench. Lettuce seedlings were transplanted into 3-liter pots filled with sand. During the spring and summer seasons experiments were conducted with and without a 18% black shade netting placed 1.5 m above the plants. Nutritional supply was provided by nutrient solution recirculating in an automatically operated irrigation system. The evaluated traits were as follows: number of leaves, fresh and dry leaf matter, stem length, stem diameter, fresh and dry stem matter, fresh and dry shoot matter, root length and fresh and dry root matter. The cultivars Gloriosa (in autumn-winter), Grandes Lagos and Gloriosa (in the spring) and Crocantela and Vera (in the summer), presented greater matter yield and are deemed the most suitable for cultivation in these seasons. The use of a shade netting within the sheltered environment did not improve the performance of the cultivars and its use is not necessary in the spring and summer.

The objective of this work was to determine the harvest interval for phytomass production of marjoram (Origanum majorana) in summer and winter transplants. Two independent experiments were performed in off-ground cultivation: one with a summer and another with a winter transplant, in a completely randomized design with five harvest intervals (30, 45, 60, 72, and 90 days) and four replicates. The fresh and dry masses of leaves, branches, and aerial part were determined. For each plant, the production accumulated in the harvests was calculated as affected by days after the transplant. The fresh matter mass of the leaves was higher at the intervals of 60 and 90 days, in the summer transplant, and of 72 and 90 days, in the winter transplant. Harvesting at intervals of 60 days in the summer transplant and of 72 days in the winter transplant are appropriate for marjoram phytomass production. Resumo: O objetivo deste trabalho foi determinar o intervalo de colheita para produção de fitomassa de manjerona (Origanum majorana), em transplantes no verão e no inverno. Foram realizados dois experimentos independentes em cultivo fora do solo: um com transplante no verão e outro no inverno, em delineamento inteiramente casualizado, com cinco intervalos de colheita (30, 45, 60, 72 e 90 dias) e quatro repetições. Foram determinadas as massas de matéria fresca e seca de folhas, ramos e parte aérea. Para cada planta, foi calculada a produção acumulada nas colheitas em função dos dias após o transplante. A massa de matéria fresca de folhas foi superior nos intervalos de 60 e 90 dias, no transplante de verão, e de 72 e 90 dias, no transplante de inverno. Colheitas em intervalos de 60 dias, no transplante de verão, e de 72 dias, no transplante de inverno, são apropriadas para produção de fitomassa de manjerona.

portuguesO objetivo deste trabalho foi determinar o tamanho otimo de parcela para avaliar a massa de materia fresca de aveia preta (Avena strigosa Schreb) e de ervilhaca (Vicia sativa L.), em cenarios formados por combinacoes de numeros de tratamentos, numeros de repeticoes e niveis de precisao. Foram conduzidos 15 ensaios de uniformidade com aveia preta e ervilhaca, em cultivo solteiro e em consorcio. Foi avaliada a massa de materia fresca em 540 unidades experimentais basicas (UEB) de 1 m × 1 m (36 UEB por ensaio). Foi estimado o indice de heterogeneidade do solo de SMITH (1938). Foi determinado o tamanho de parcela por meio do metodo de HATHEWAY (1961) em cenarios formados pelas combinacoes de i tratamentos (i = 5, 10, 15 e 20), r repeticoes (r = 3, 4, 5, 6, 7 e 8) e d niveis de precisao (d = 2%, 4%, 6%, 8%, 10%, 12%, 14%, 16%, 18% e 20%). Para avaliar a massa de materia fresca de aveia preta e de ervilhaca, em cultivo solteiro ou em consorcio, nos delineamentos inteiramente casualizado e de blocos completos ao acaso, com 5 a 20 tratamentos e com cinco repeticoes, parcelas de 10 m2 sao suficientes para identificar diferencas significativas entre tratamentos, a 0,05 de probabilidade, de 10% da media geral do experimento EnglishThe aim of this study was to determine the optimal plot size for evaluating the fresh weight of black oats (Avena strigosa Schreb) and the common vetch (Vicia sativa L.) in scenarios comprising combinations of the number of treatments, number of replications and levels of precision. Fifteen uniformity trials were conducted with single-crop and intercropped black oats and vetch. Fresh weight was evaluated in 540 basic experimental units (BEU), each of 1 m × 1 m (36 BEU per trial). The Smith index of soil heterogeneity (1938) was estimated. Plot size was determined using the HATHEWAY method (1961), in scenarios comprising combinations of i treatments (i = 5, 10, 15 and 20), r replications (r = 3, 4, 5, 6, 7 and 8) and d levels of precision (d = 2%, 4%, 6%, 8%, 10%, 12%, 14%, 16%, 18% and 20%). To evaluate the fresh weight of monocropped or intercropped black oats and vetch in a completely randomized or randomized complete block design, with from 5 to 20 treatments and five replications, plots of 10 m2 are sufficient to identify, at a probability of 0.05, significant differences between treatments of 10% of the overall mean value of the experiment

O objetivo deste trabalho foi determinar o tamanho de amostra (número de cápsulas) necessário para a estimação da média de caracteres produtivos de linho (Linum usitatissimum L.), cultivar CDC Normandy, em níveis de precisão. Em área experimental de 15m×15m (225 m2) aos 137 dias após a semeadura, foram selecionadas, aleatoriamente, 300 plantas e coletada uma cápsula por planta. Em cada cápsula foram avaliados os caracteres massa de cápsula, massa de grãos por cápsula, número de grãos por cápsula e massa de mil grãos. Para cada caractere, foram calculadas medidas de tendência central, variabilidade, assimetria e curtose. Foi determinado o tamanho de amostra por meio de reamostragem, com reposição, de 10.000 reamostras. Para a estimação da média desses caracteres de linho, cultivar CDC Normandy, com amplitude do intervalo de confiança de 95% igual a 10% da estimativa da média são necessárias 78 cápsulas.

The aim of this study was to determine the sample size (i.e., number of plants) required to estimate the mean and median of flax traits (Linum usitatissimum L.) of the cultivar CDC Normandy, with precision levels. In experimental area of 15 × 15 m (225 m2) at 134 days after sowing, 300 plants were collected randomly. In each plant, it was measured morphological (plant height and number of branches) and productive traits (number of capsules, fresh matter of capsules, fresh matter of aerial part without capsules, fresh matter of aerial part, dry matter of capsules, dry matter of aerial part without capsules, and dry matter of aerial part). For each trait, it was calculated measures of central tendency, variability, skewness, and kurtosis. It was determined the sample size by resampling with replacement of 10,000 resamples. In order to estimate the mean of morphological and pro­ductive traits of flax, cultivar CDC Normandy, with the amplitude of the confidence interval of 95% equal to 30% of the estimated mean, 81 plants are required. To estimate the median, with the same precision, it is necessary 161 plants.

The influence of the basic experimental unit size on the plot size estimation determined by the method of maximum curvature of the coefficient of variation model is unknown in sunn hemp. This study aimed to verify the influence of the basic experimental unit (BEU) size in the estimate of the optimum plot size obtained by the method of maximum curvature of the coefficient of variation model for the evaluation of fresh matter of sunn hemp (Crotalaria juncea L.). Fresh matter of sunn hemp at the flowering was evaluated in uniformity trials in two sowing dates. In each sowing date, 4,608 BEU of 0.5 × 0.5 m (0.25 m2) were evaluated and 64 BEU plans were formed with sizes from 0.25 to 64 m2. In each evaluation period for each BEU plan, the first order spatial autocorrelation coefficient, variance, standard deviation, mean, coefficient of variation of the trial and the plot size were determined with the fresh matter data. For each BEU plan, the optimum plot size was determined by the method of maximum curvature of the coefficient of variation model. The estimate of optimum plot size depends on the basic experimental unit size. Determining the plot size to assess the fresh matter in basic experimental units as small as possible is recommended in order to prevent overestimation of the plot size and to contemplate all existing variability. Key words: Crotalaria juncea L., experimental design, basic experimental unit.

RESUMO Os objetivos deste trabalho foram avaliar as relações lineares entre caracteres de linho (Linum usitatissimum L.) e identificar caracteres para a seleção indireta. Em área experimental de 15 × 15 m (225 m2), aos 134 dias após a semeadura, foram selecionadas, aleatoriamente, 300 plantas. Em cada planta, foram mensurados os caracteres altura de planta, número de ramos, número de cápsulas, massa verde de cápsulas, massa verde de parte aérea sem cápsulas, massa verde de parte aérea, massa seca de cápsulas, massa seca de parte aérea sem cápsulas e massa seca de parte aérea. Para cada caractere, foi calculada a média e o coeficiente de variação. Foi investigada a relação linear entre os caracteres por meio de análises de correlação e de trilha. Na cultura de linho, o número de cápsulas tem relação linear positiva com as massas verde e seca de cápsulas e de parte aérea e pode ser utilizado para seleção indireta. ABSTRACT The objectives of this study were to evaluate the linear relations among traits of flax (Linum usitatissimum L.) and identify traits for indirect selection. In experimental area of 15 × 15 m (225 m2) 300 plants were randomly collected at 134 days after seeding. The traits plant height, number of branches, number of capsules, fresh matter of capsules, fresh matter of aerial part without capsules, fresh matter of aerial part, dry matter of capsules, dry matter of aerial part without capsules, and dry matter of aerial part were measured in each plant. The mean and coefficient of variation were calculated for each trait. It was studied the linear relation among the traits through correlation and path analysis. In flax, the number of capsules has positive linear relation with fresh and dry matter of capsules and aerial part and it can be used for indirect selection.

The determination of the optimum plot size in agricultural crops is important for obtaining accurate inferences in the treatments in question. This study aimed at determining the optimum plot size (Xo) and the number of replications to evaluate the fresh matter (FM) and the dry matter (DM) of oat and at verifying the variability of Xo among cultivars and sowing dates. Ninety-six uniformity trials of 3×3 m were performed and each assay was divided into 36 basic experimental units (BEU) of 0.5×0.5 m. The 96 uniformity trials were distributed in four cultivars and three sowing dates. At the flowering stage, FM and DM were determined in each BEU. Then, the Xo was determined in each uniformity assay, using the maximum curvature method of the coefficient of variation model. In oat, there is variability of Xo among cultivars and sowing dates to measure FM and DM. For the four cultivars on the three sowing dates, the Xo of 1.66 m2 and of 1.73 m2 are suitable to evaluate FM and DM, respectively. Four replications to evaluate the maximum of 50 treatments in completely randomized design and randomized blocks design are sufficient so that the differences among treatment means of 44.75% of the experiment mean may be significant, using the Tukey test at 5% probability to measure FM and DM in oat.

This study aims to determine the most suitable model to estimate the leaf area of dwarf pigeon pea in function of the leaf central leaflet dimension. Six samplings of 200 leaves were performed in the first experiment, at 36, 42, 50, 56, 64, and 72 days after emergence (DAE). In the second experiment, seven samplings of 200 leaves were performed at 29, 36, 43, 49, 57, 65, and 70 DAE, totaling 2600 leaves. The length (L) and width (W) of the central leaflet were measured in all leaves composed by left, central, and right leaflets, the product of length times width (LW) was calculated, and the leaf area (Y – sum of left, central, and right leaflet areas) was determined by digital images. Linear, power, quadratic, and cubic models of Y as function of L, W, and LW were built using data from the second experiment. Leaves from the first experiment were used to validate the models. In dwarf pigeon pea, the linear (Ŷ = – 0.4088 + 1.6669x, R2 = 0.9790) is preferable, but power (Ŷ = 1.6097x1.0065, R2 = 0.9766), quadratic (Ŷ = – 0.3625 + 1.663x + 0.00007x2, R2 = 0.9790), and cubic (Ŷ = 0.7216 + 1.522x + 0.005x2 – 5E–05x3, R2 = 0.9791) models in function of LW are also suitable to estimate the leaf area obtained by digital images. The power model (Ŷ = 5.2508x1.7868, R2 = 0.95) based on the central leaflet width is less laborious because requires only one variable, but it presents accuracy reduction.

EnglishThis study aimed to verify the influence of the basic experimental unit (BEU) size in the estimation of the optimum plot size to evaluate the fresh matter of sunn hemp (Crotalaria juncea L.) using the modified maximum curvature method. The fresh matter of sunn hemp was evaluated in uniformity trials in two sowing season in flowering. In each sowing season, 4,608 BEUs of 0.5×0.5m (0.25m2) were evaluated and 36 BEU plans were formed with sizes from 0.25 to 16m2. In each evaluation period for each BEU plan, using fresh matter data, optimum plot size was estimated through the modified maximum curvature method. Estimation of the optimum plot size depends on the BEU size. Assessing fresh matter in BEUs that are as small as possible is recommended in order to use it to estimate the optimum plot size. Key words: Crotalaria juncea L.; modified maximum curvature; uniformity trials; experimental planing. portuguesO objetivo deste trabalho foi verificar a influencia do tamanho da unidade experimental basica (UEB) na estimativa do tamanho otimo de parcela, para a avaliacao da massa de materia verde de crotalaria juncea (Crotalaria juncea L.), pelo metodo da maxima curvatura modificado. Avaliou-se a massa de materia verde de crotalaria juncea, no florescimento da cultura, em ensaios de uniformidade conduzidos em duas epocas de semeadura. Em cada epoca foram avaliadas 4.608 UEB de 0,5×0,5m (0,25m2) e formaram-se 36 planos de UEB com tamanhos entre 0,25 e 16m2. Em cada epoca, para cada plano de UEB, com os dados de massa de materia verde, estimou-se o tamanho otimo de parcela, pelo metodo da maxima curvatura modificado. A estimativa do tamanho otimo de parcela depende do tamanho da unidade experimental basica. E indicado avaliar a massa de materia verde em UEB de menor tamanho possivel, para serem usadas na estimacao do tamanho otimo de parcela. Palavras-chave: Crotalaria juncea L.; maxima curvatura modificado; ensaios de uniformidade; planejamento experimental.

The aim of this study was to determine the optimum plot size to evaluate the fresh matter of aerial part of dwarf pigeon pea (Cajanus cajan (L.) Millsp), cultivar IAPAR 43 (Arata), in scenarios formed by combinations of numbers of treatments, number of replications, and precision levels. The fresh matter of aerial part was weighed on basic experimental units of 1 m × 1 m in three uniformity trials with size of 24 m × 12 m (288 m2 in each trial). The soil heterogeneity index of Smith was estimated. Also, the optimum plot size was determined by Hatheway’s method in scenarios formed by combinations of i treatments (i = 5, 10, 15, and 20), r replications (r = 3, 4, 5, 6, 7 8, 9, and 10), and d precision levels (d = 5%, 10%, 15%, 20%, 25%, and 30%). In experiments designed on randomized block design with 5 to 20 treatments and four replications, plots with 9 m2 were enough to identify significant differences among treatments regarding the fresh matter of aerial part in dwarf pigeon pea at 5% probability of 30% of the experiment overall mean.

Os objetivos deste trabalho foram determinar o tamanho ótimo de parcela e o número de repetições, para avaliar a massa verde de ervilha forrageira (Pisum sativum subsp. arvense (L.) Poir). Foram realizados 27 ensaios de uniformidade de 5m×5m (25m2). Cada ensaio foi dividido em 25 unidades experimentais básicas (UEB) de 1m×1m, totalizando 675UEB. Foi pesada a massa verde das plantas de cada UEB. Nove ensaios (225UEB) foram avaliados aos 92 dias após a semeadura (DAS), nove ensaios (225UEB) foram avaliados aos 98 DAS e os outros nove ensaios (225UEB) aos 106 DAS. O tamanho ótimo de parcela (Xo) foi determinado por meio do método da curvatura máxima do modelo do coeficiente de variação e as comparações de médias, entre as épocas de avaliação, foram feitas pelo teste t de Student. O número de repetições, para experimentos nos delineamentos inteiramente casualizado e blocos ao acaso, em cenários formados pelas combinações de i tratamentos (i=3, 4, ..., 50) e d diferenças mínimas entre médias de tratamentos a serem detectadas como significativas a 5% de probabilidade, pelo teste de Tukey, expressas em percentagem da média do experimento (d=10%, 12%, ..., 30%), foi determinado por processo iterativo até a convergência. O tamanho ótimo de parcela para avaliar a massa verde de ervilha forrageira é de 5,03UEB de 1m2 (5,03m2). Quatro repetições, para avaliar até 50 tratamentos, nos delineamentos inteiramente casualizado e blocos ao acaso, são suficientes para identificar, como significativas a 5% de probabilidade, pelo teste de Tukey, diferenças entre médias de tratamentos de 32,4% da média do experimento. The objectives of this research were to determine the optimum plot size and number of repetitions and to evaluate the fresh weight of forage pea (Pisum sativum subsp. arvense (L.) Poir). Twenty-seven uniformity trials of 5m×5m (25m2) were conducted. Each trial was divided in 25 basic experimental units (UEB) of 1m×1m, totaling 675UEB. The fresh weight of plants, in each UEB was weighed. Nine trials (225UEB) were evaluated at 92 days after sowing, nine trials (225UEB) at 98 days after sowing and the other nine trials (225UEB) at 106 days after sowing. The optimum plot size (Xo) was determined by the method of maximum curvature of the model coefficient of variation and the means compared, among evaluation times, by Student's t test. The number of repetitions for experiments on completely randomized and randomized block designs, in scenarios of combinations of i treatments (i=3, 4, ..., 50) and d minimal differences between treatments means, to be detected as significant, 5% probability by Tukey test, expressed in percentage of the average of the experiment (d=10%, 12%, ..., 30%), was determined by interative process until convergence. The optimum plot size to evaluate the fresh weight of forage pea is 5.03UEB was of 1m2 (5.03m2). Four replications, to evaluate up to 50 treatments, in completely randomized and randomized block designs, are sufficient to identify, as significant at the 5% probability by Tukey test, differences between treatment means 32.4% of the average experiment.

This study aimed to fit the Gompertz and Logistic growth models to evaluate the description of fresh and dry masses of shoot as a function of accumulated thermal sum and accumulated solar radiation, to compare the fittings, and to indicate which one best describes the growth of two sudangrass cultivars at four sowing times. Eight uniformity trials were conducted with the sudangrass crop. Five plants were collected from each trial for weighing of fresh and dry shoot masses. These evaluations were carried out three times a week starting from 15 days after plant emergence. The Gompertz and Logistic models were fitted to the masses as a function of accumulated thermal sum and accumulated solar radiation. The parameters and their confidence intervals were estimated. The points of maximum acceleration, inflection, maximum deceleration and asymptotic deceleration, and fit quality indicators were calculated. The intrinsic nonlinearity and the parameter-effects nonlinearity were quantified. The independent variables accumulated thermal sum and accumulated solar radiation can be used to fit the models. Both models satisfactorily describe the growth of fresh and dry shoot masses of cultivars BRS Estribo and CG Farrapo. The Logistic model is more accurate.

Adjusting nonlinear Gompertz and Logistic models will help in the understanding of the growth pattern of the rye crop and also in the height response of the plant, when planted in different environmental conditions. The the aims of this study were to adjust the nonlinear Gompertz and Logistic models for plant height and indicate the one that best describes growth of two rye cultivars in five sowing times. Ten uniformity trials were conducted with the rye crop in the 2016 harvest. In each trial, ten randomly selected plants were evaluated from the first expanded leaf weekly. In each plant height was measured. The adjustment of the Gompertz and Logistic models as a function of the accumulated thermal sum was performed with the average plant height at each evaluation. The parameters a, b, and c were estimated for each model. The confidence interval for each parameter and the inflection points, maximum acceleration, maximum deceleration and asymptotic deceleration were calculated. The quality of fit of the models was verified by the coefficient of determination, Akaike's information criterion and residual standard deviation. Intrinsic non-linearity and non-linearity of the parameter effect were quantified. Both models describe satisfactorily the plant height. The model that best describes the growth of rye cultivars is Logistic.

The aim of this study was to determine the sample size (i.e., number of plants) required to estimate the mean and median of canola (Brassica napus L.) traits of the Hyola 61, Hyola 76, and Hyola 433 hybrids with precision levels. At 124 days after sowing, 225 plants of each hybrid were randomly collected. In each plant, morphological (plant height) and productive traits (number of siliques, fresh matter of siliques, fresh matter of aerial part without siliques, fresh matter of aerial part, dry matter of siliques, dry matter of aerial part without siliques, and dry matter of aerial part) were measured. For each trait, measures of central tendency, variability, skewness, and kurtosis were calculated. Sample size was determined by resampling with replacement of 10,000 resamples. The sample size required for the estimation of measures of central tendency (mean and median) varies between traits and hybrids. Productive traits required larger sample sizes in relation to the morphological traits. Larger sample sizes are required for the hybrids Hyola 433, Hyola 61, and Hyola 76, in this sequence. In order to estimate the mean of canola traits of the Hyola 61, Hyola 76 e Hyola 433 hybrids with the amplitude of the confidence interval of 95% equal to 30% of the estimated mean, 208 plants are required. Whereas 661 plants are necessary to estimate the median with the same precision.

The objectives of this study were to determine the optimum plot size (Xo) and the number of replications to evaluate the grains yield of rye (Secale cereale L.) and investigate the variability of Xo between two cultivars and three sowing dates. Eighteen uniformity trials were conducted with rye. The Xo was determined by the method of maximum curvature of the coefficient of variation model. The number of repetitions was determined in scenarios formed by combinations of i treatments (i = 3, 4, ... 50) and d minimum differences between means of treatments to be detected as significant at 0.05 of probability, by Tukey test, expressed in percentage of the average of the experiment (d = 10, 12, ... 30%). There is variability in optimum plot size to evaluate the grains yield among the cultivars BRS Progresso and Temprano and among sowing dates in the rye crop. The optimum plot size to evaluate the grains yield of rye is 6.08 m2. Seven replicates are sufficient to evaluate the grains yield of rye in experiments with up to 50 treatments, and identify, as significant at 5% probability by Tukey test, differences among averages of treatments of 29.65% of the mean of the experiment in designs completely randomized and randomized block.

RESUMO - Os objetivos foram determinar o tamanho de amostra para estimacao da media de caracteres de milheto, para distintos niveis de precisao, e verificar a variabilidade do tamanho de amostra entre epocas de avaliacao. Foi conduzido um ensaio de uniformidade com milheto, no ano agricola 2012/2013. Foram marcadas, aleatoriamente, 360 plantas. Aos 26, 33, 40 e 48 dias apos a semeadura foram mensurados os caracteres altura de planta, diâmetro do colmo, numero de afilhos, nos por colmo e nos por afilho. Aos 48 dias apos a semeadura foram pesadas a massa verde de parte aerea e a massa seca de parte aerea. Para cada caractere, foram calculadas as medidas de tendencia central e de variabilidade. Foi determinado o tamanho de amostra por reamostragem, com reposicao, para as amplitudes do intervalo de confianca de 95% iguais a 15%, 16%, .., 30% da estimativa da media. Para estimacao da media de caracteres de milheto, com amplitude do intervalo de confianca de 95% de ate 30% da estimativa da media, sao necessarias 193 plantas. Ha variabilidade no tamanho de amostra para os caracteres altura de planta, diâmetro do colmo, numero de afilhos, nos por colmo e nos por afilho entre as epocas de avaliacao. Palavras-chave: Pennisetum glaucum, dimensionamento amostral, reamostragem, precisao experimental. SAMPLE SIZE TO ESTIMATE THE MEAN OF MILLET TRAITS IN EVALUATION TIMES ABSTRACT - The objectives of this work were to determine the sample size for the estimation of the mean of millet traits, for different levels of precision, and to verify the variability of sample size among evaluation times. An uniformity trial was performed with millet during the 2012/2013 agricultural year. A total of 360 plants were marked randomly. At 26, 33, 40, and 48 days after sowing, the traits plant height, stem diameter, number of tillers, nodes per stem, and nodes per tiller were measured. At 48 days after sowing, the fresh matter of aerial part and the dry matter of aerial part were weighed. Measures of central tendency and variability were calculated for each trait. The sample size was determined by resampling with replacement of 10,000 resamples for amplitudes of the confidence interval of 95% equal to 15%, 16%, ..., 30% of the estimated mean. In order to estimate the mean of pearl millet characters with the amplitude of the confidence interval of 95% up to 30% of the estimated mean, 193 plants are required. There is variability in sample size for the traits plant height, stem diameter, number of tillers, nodes per stem and nodes per tiller among evaluation times. Keywords: Pennisetum glaucum, sample dimension, resampling, experimental precision.

Os objetivos deste trabalho foram determinar o tamanho ótimo de parcela e o número de repetições, para avaliar a massa verde de canola (Brassica napus L.). Foram realizados 27 ensaios de uniformidade de 5m×5m (25m2), sendo nove ensaios para cada um dos seguintes híbridos: Hyola 61, Hyola 76 e Hyola 433. Cada ensaio foi dividido em 25 unidades experimentais básicas (UEB) de 1m×1m, totalizando 675 UEB. Foi pesada a massa verde das plantas de cada UEB. O tamanho ótimo de parcela (Xo) foi determinado por meio do método da curvatura máxima do modelo do coeficiente de variação, e as comparações de médias, entre os híbridos, foram feitas pelo teste de Scott-Knott. O número de repetições, para experimentos nos delineamentos inteiramente casualizados e blocos ao acaso, em cenários formados pelas combinações de i tratamentos (i=3, 4, ..., 50) e d diferenças mínimas entre médias de tratamentos a serem detectadas como significativas a 5% de probabilidade, pelo teste de Tukey, expressas em percentagem da média do experimento (d=10%, 13%, ..., 40%), foi determinado por processo iterativo até a convergência. O tamanho ótimo de parcela para avaliar a massa verde de canola é 6,41m2. Quatro repetições, para avaliar até 50 tratamentos, nos delineamentos inteiramente casualizados e blocos ao acaso, são suficientes para identificar, como significativas a 5% de probabilidade, pelo teste de Tukey, diferenças entre médias de tratamentos de 41,4% da média do experimento. The objectives of this work were to determine the optimum plot size and number of repetitions, to evaluate the fresh weight of canola (Brassica napus L.). Twenty-seven uniformity trials of 5m×5m (25m2) were conducted. Each trials was divided in 25 basic experimental units (BEU) of 1m×1m, totaling 675BEU. The fresh weight of plants, in each BEU was weighed. The optimum plot size (Xo) was determined by the method of maximum curvature of the model coefficient of variation and the means compared, among hybrids, by Scott-Knott test. The number of repetitions, for experiments on completely randomized and randomized block designs, in scenarios of combinations of i treatments (i=3, 4, ..., 50) and d minimal differences between treatments means, to be detected as significant, 5% probability by Tukey test, expressed in percentage of the average of the experiment (d=10%, 12%, ..., 40%), was determined by iterative process until convergence. The optimum plot size to evaluate the fresh weight of canola is 6.41 m2. Four replications, to evaluate up to 50 treatments, in completely randomized and randomized block designs, are sufficient to identify, as significant at the 5% probability by Tukey test, differences between treatment means 41.4% of the average experiment.

The objective of the present study was to fit Gompertz and Logistic nonlinear to descriptions of morphological traits of sunn hemp. Two uniformity trials were conducted and the crops received identical treatment in all experimental area. Sunn hemp seeds were sown in rows 0.5 m apart with a plant density of 20 plants per row meter in a usable area of 52 m × 50 m. The following morphological traits were evaluated: plant height (PH), number of leaves (NL), stem diameter (SD), and root length (RL). These traits were assessed daily during two sowing periods—seeds were sown on October 22, 2014 (first period) and December 3, 2014 (second period). Four plants were randomly collected daily, beginning 7 days after first period and 13 days after for second period, totaling 94 and 76 evaluation days, respectively. For Gompertz models the equation was used y=a*e^((?-e?^((b-c*xi))and Logistic models the equation was used yi= a/(1+e^((-b-c*xi)). The inflection points of the Gompertz and Logistic models were calculated and the goodness of fit was quantified using the adjusted coefficient of determination, Akaike information criterion, standard deviation of residuals, mean absolute deviation, mean absolute percentage error, and mean prediction error. Differences were observed between the Gompertz and Logistic models and between the experimental periods in the parameter estimate for all morphological traits measured. Satisfactory growth curve fittings were achieved for plant height, number of leaves, and stem diameter in both models using the evaluation criteria: coefficient of determination (R²), Akaike information criterion (AIC), standard deviation of residuals (SDR), mean absolute deviation (MAD), mean absolute percentage error (MAPE), and mean prediction error (MPE).